Inventiones mathematicae

, Volume 93, Issue 1, pp 35-76

First online:

Tannaka-Krein duality for compact matrix pseudogroups. TwistedSU(N) groups

  • S. L. WoronowiczAffiliated withInstituut voor Theoretische Fysica, Universität Leuven

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The notion of concrete monoidalW *-category is introduced and investigated. A generalization of the Tannaka-Krein duality theorem is proved. It leads to new examples of compact matrix pseudogroups. Among them we have twistedSU(N) groups denoted byS μ U(N). It is shown that the representation theory forS μ U(N) is similar to that ofSU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.